Question

A dentist drill starts at rest and spins up to 12,000 rpm in 2.1 seconds and then remains at that level for 20 seconds. What is the angular acceleration of the drill?

1) 6000 rad/s²
2) 5714 rad/s²
3) 5714 rpm/s
4) 6000 rpm/s

Answer 1

The angular acceleration of the dentist drill is approximately 5714 rad/s².

Step-by-step explanation:

To find the angular acceleration of the dentist drill, we first need to convert rpm to rad/s. Since 1 rpm is equal to (2π/60) rad/s, the drill's final angular velocity is (12000 × 2π/60) rad/s = 400π rad/s. Using the formula ω = ω0 + αt, where ω0 is the initial angular velocity, ω is the final angular velocity, α is the angular acceleration, and t is the time, we can calculate the initial angular velocity:

(400π) = 0 + α × 2.1

α ≈ 5714 rad/s²

Therefore, the angular acceleration of the drill is approximately 5714 rad/s². Hence, the correct answer is option 2) 5714 rad/s².